WEIPING ZHANG 
Department of Statistics and Finance
University of Science and Technology of China
“A Joint Modeling Approach for Longitudinal Studies”
ABSTRACT
In longitudinal studies, it is of fundamental importance to understand the dynamics in the mean function, variance function, and correlations of the repeated or clustered measurements. For modeling the covariance structure, Cholesky type decomposition based approaches are demonstrated effective. However, parsimonious approaches for directly revealing the correlation structure among longitudinal measurements remain less explored, and existing joint modeling approaches may encounter difficulty in interpreting the covariation structure. In this paper, we propose a novel joint mean-variance-correlation modeling approach for longitudinal studies. By applying hyperspherical coordinates, we obtain an unconstrained parametrization for the correlation matrix that automatically guarantees its positive definiteness, and develop a regression approach to model the correlation matrix of the longitudinal measurements by exploiting the parametrization. The proposed modeling framework is parsimonious, interpretable, and flexible for analyzing longitudinal data. Extensive data examples and simulations support the effectiveness of the proposed approach.
